The Numbers of Nature's Code

Assuming that Nature is described by a universal rewrite system and operates according to a process that we can refer to as Nature's code, we define certain numbers as being crucial indicators of how the code operates, whether in biology, chemistry or physics. We also show how these numbers originate in the most extraordinarily simple way from two numbers which correspond to the two distinct processes - conserve and create - within the system which can in tum be related to the properties of duality and anticommutativity. The numbers emerge in a number of distinct series which have distinct algebraic and geometrical representations. The geometrical structures translate easily from 3- to higher-dimensional representations, especially those of dimension 4 and 8, and also connect significantly with rotational symmetries and with Lie groups, up to E₈. The fundamental particles of physics are a classic case of the operation of the number series, in which all the significant numbers are represented, and no others. The structure leads to a complete classification of fermions and bosons within an overall E₈ representation. An almost parallel system emerges in the genetic code, leading to the processes of transcription and translation.